In most conventional air-conditioning systems, the duty-cycle of the compressor and its associated indoor fan are identical. That is, when the compressor starts, the fan starts. When the compressor is stopped, the fan simultaneously stops. This kind of duty cycle control is somewhat inefficient in that a considerable amount of "cold" is left in the cooling coil and ducts after the compressor is shut off. Some of this cold is dissipated to the outside atmosphere unless the indoor fan is kept running for some time after the compressor is stopped.
There are certain other air cooling control systems on the market which function in the just-described manner and do in fact continue to run the indoor fan for a given time after the compressor shuts off. However, to the best of my knowledge, these systems are relatively expensive and require changes or additions in the existing wiring.